Related papers: Global heteroclinic rebel dynamics among large 2-c…
We study patterns that arise in the wake of an externally triggered, spatially propagating instability in the complex Ginzburg-Landau equation. We model the trigger by a spatial inhomogeneity moving with constant speed. In the comoving…
Conditions are provided under which lack of domination of a homoclinic class yields robust heterodimensional cycles. Moreover, so-called viral homoclinic classes are studied. Viral classes have the property of generating copies of…
We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\mathcal H_N = p_1^2 + p_2^2 +\sum_{n=1}^N \gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\gamma_n$…
Motivated by recent experimental progress in the context of ultra-cold multi-color fermionic atoms in optical lattices, we have developed a method to exactly diagonalize the Heisenberg $SU(N)$ Hamiltonian with several particles per site…
This work examines the global dynamics of classical solutions of a two-stage (juvenile-adult) reaction-diffusion population model in time-periodic and spatially heterogeneous environments. It is shown that the sign of the principal…
We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry.…
Almost equitable partitions (AEPs) have been linked to cluster synchronization in oscillatory systems, highlighting the importance of structure in collective network dynamics. We provide a general spectral framework that formalizes this…
In this paper, we investigate saddle-node to saddle separatrix--loops that we term SNICeroclinic bifurcations. They are generic codimension-two bifurcations involving a heteroclinic loop between one non-hyperbolic and one hyperbolic saddle.…
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, $p\nearrow p_{c}$. To this end, we…
Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making…
In this work we launch a systematic theory of superconformal blocks for four-point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
It is well known that the allowed wavefunctions for an $N$-electron system should be antisymmetric with respect to the permutation of any pair of electron labels. On the other hand, the Hamiltonian for such system is invariant under any…
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit…
We study the bifurcations and phase diagram for a network of identical Kuramoto oscillators with a coupling that explicitly breaks the rotational symmetry of the equations. Applying the Watanabe-Strogatz ansatz, the original N-dimensional…
In Fermionic Molecular Dynamics antisymmetrized products of Gaussian wave packets are projected on angular momentum, linear momentum, and parity. An appropriately chosen set of these states span the many-body Hilbert space in which the…
Within the supertwistor approach, we analyse the superconformal structure of 4D N = 2 compactified harmonic/projective superspace. In the case of 5D superconformal symmetry, we derive the superconformal Killing vectors and related building…
We present a general method for studying front propagation in nonlinear systems with a global constraint in the language of hybrid tank models. The method is illustrated in the case of semiconductor superlattices, where the dynamics of the…